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Metamath Proof Explorer

Theorem isidom

Description: An integral domain is a commutative domain. (Contributed by Mario Carneiro, 17-Jun-2015)

Ref Expression
Assertion isidom ⊢ R ∈ IDomn ↔ R ∈ CRing ∧ R ∈ Domn

Proof

Step Hyp Ref Expression
1 df-idom ⊢ IDomn = CRing ∩ Domn
2 1 elin2 ⊢ R ∈ IDomn ↔ R ∈ CRing ∧ R ∈ Domn